Oscillator Requirements

Transcription

1 Oscillator Design Introduction What makes an oscillator? Types of oscillators Fixed frequency or voltage controlled oscillator LC resonator Ring Oscillator Crystal resonator Design of oscillators Frequency control, stability Amplitude limits Buffered output isolation Bias circuits Voltage control Phase noise 1

2 Oscillator Requirements Power source Frequency-determining components Active device to provide gain Positive feedback LC Oscillator Hartley Colpitts RC Ring f r = 1/ 2π LC Crystal Clapp Wien-Bridge 2

3 xi Feedback Model for oscillators A xo A f ( j ) ω = 1 A A( jω) ( jω) β( jω) x f x = x + d i β x f Barkhausen A criteria ( jω) β ( jω) = 1 Barkhausen s criteria is necessary but not sufficient. If the phase shift around the loop is equal to 360 o at zero frequency and the loop gain is sufficient, the circuit latches up rather than oscillate. To stabilize the frequency, a frequency-selective network is added and is named as resonator. Automatic level control needed to stabilize magnitude 3

4 General amplitude control One thought is to detect oscillator amplitude, and then adjust Gm so that it equals a desired value By using feedback, we can precisely achieve GmRp = 1 Issues Complex, requires power, and adds noise 4

5 Leveraging Amplifier Nonlinearity as Feedback Practical trans-conductance amplifiers have saturating characteristics Harmonics created, but filtered out by resonator Our interest is in the relationship between the input and the fundamental of the output As input amplitude is increased Effective gain from input to fundamental of output drops Amplitude feedback occurs! (GmRp = 1 in steady-state) 5

6 Negative-Resistance Model Z a ( s) ( s) Z r Equivalent Circuit Active Circuit Resonator GL GM Oscillation: [ Z ( s) ] + Z ( s) Re Re[ ] = 0 a r 6

7 Resonator with series resisters Perform equivalent parallel conversion Warning: in practice, RLC networks can have secondary (or more) resonant frequencies, which cause undesirable behavior Equivalent parallel network masks this problem in hand analysis Simulation will reveal the problem 7

8 LC Oscillators LC tank circuit as a resonator to control frequency. High Q resonator provides good stability, low phase noise Frequency adjusted by voltage using varactor diodes in the resonator. For oscillation to begin, open loop gain Aβ 1. 8

9 Tuned Amplifier V out = -g m R P v gs The impedance of the resonator peaks (= Rp) and the phase is 0 o at ω 0. The susceptances of the L and C cancel at resonance. 9

10 PMOS Oscillator Model Y = 1 R L + G o + sc + 1 sl = 1 R P + sc + 1 sl = R P 2 LCs + Ls R Ls P + R P V out Open loop transfer function: V in Z G m G o G Y m G m = 2 RP LCs R + P At resonance: Ls Ls + R P βv out G G 2 m m P LCs = 1 = = Y R Ls Ls G m R P One zero at s=0 Two poles at: s 1 2R P C ± 1 LC 10

11 Closed loop root locus as G m changes Root locus plot allows us to view closed loop pole locations as a function of open loop poles/zero and open loop gain (GmRp) As gain (GmRp) increases, closed loop poles move into right half S-plane 11

12 When G m R P < 1 Closed loop poles end up in the left half S-plane Under-damped response occurs Oscillation dies out 12

13 When G m R P > 1 Closed loop poles end up in the right half S-plane Unstable response occurs Waveform blows up! 13

14 When G m R P = 1 Closed loop poles end up on jω axis Oscillation maintained Issues G m R p needs to exactly equal 1, discussed earlier How do we get positive feedback 14

15 Connect two in series and add feedback If (g m R P ) 2 1, this circuit will oscillate. It can only oscillate at ω0, because only at that frequency will we have a total phase shift of 0 o. The oscillations will begin when the noise inherent in the transistors is amplified around the loop. The strength of the oscillations will build exponentially with time. The small signal analysis doesn t provide a limit to this growth. The amplitude will reach a limit either by voltage or current. 15

16 Time domain response 16

17 Cross-coupled Oscillator: Redrawn This representation emphasizes the differential topology. The two outputs are 180 degrees out of phase. This can be very useful for many applications driving a Gilbert cell mixer, for example. 17

18 Cross-coupled pair with bias I 0 provides oscillation amplitude control But it adds noise. 18

19 A popular LC oscillator Simple topology Differential implementation (good for feeding differential circuits) Good phase noise performance can be achieved 19

20 Voltage Controlled Oscillators (LC) Variable capacitor (varactor) controls oscillation frequency by adjusting V cont Much fixed capacitance cannot be removed Fixed cap lowers frequency tuning range 20

21 Voltage to Frequency Mapping Model VCO in a small signal manner Assume linear relationship in small signal Deviations in frequency proportional to control voltage variation f = K v v in 21

22 Voltage to phase Phase is integration of frequency variation Φ out = 2πK s v v in 22

23 The MOS Varactor Consists of a MOS transistor with drain and source connected together Abrupt shift in capacitance as inversion channel forms Advantage Easily integrated in CMOS Disadvantage Q is relatively low in the transition region Note that large signal is applied to varactor Transition region will be swept across each VCO cycle 23

24 Increasing Q of MOS Varactor High Q metal caps are switched in to provide coarse tuning Low Q MOS varactor used to obtain fine tuning See Hegazi et. al., A Filtering Technique to Lower LC Oscillator Phase Noise, JSSC, Dec 2001, pp

25 Hartley Oscillator Uses a tapped inductor Not popular for IC implementations 25

26 COLPITTS Similar to Hartley oscillator Tapped ground in capacitor circuit 26

27 Colpitts Oscillator Open-loop for analysis A= V2/v1 = g m R p at ω 0 β=v1 /v2 = C1/(C1+C2) 27

28 Colpitts with gain and phase control R E can help reduce the phase shift by making r e + R E >> ωc2. This will also reduce the loop gain. 28

29 CLAPP OSCILLATOR Modified Colpitts oscillator Modification done to improve stability 29

30 CRYSTAL OSCILLATOR Uses crystal for frequencydetermining component (parallel) Uses crystal in feedback path to frequency determining components (series) Very stable circuit 30

31 RC OSCILLATOR Generates a sine wave Uses phase shift of RC network for required circuit phase shift Uses three RC segments Low stability f = 1/ 2πRC 6 r 31

32 Ring Oscillator Single ended Require odd number of stages Each stage provides 180/n phase shift Gain = 1 by saturation 32

33 Twisted Ring Differential Ring Oscillator Common mode rejection of substrate coupled noise Easy to control the delay Can use an odd or even number of stages quadrature or polyphase signals Popular delay cell: Maneatis delay cell Maneatis et. al., Precise Delay Generation Using Coupled Oscillators, JSSC, Dec 1993 (look at pp for delay cell description) All ring oscillators have large noise as compared to LC oscillators 33

34 Maneatis delay cell Good power supply rejection Good substrate noise rejection Low jitter 34

35 Maneatis delay cell bias circuit 35

36 WIEN-BRIDGE Simple, Stable, Popular Uses resistor and capacitor Uses two RC networks connected to the positive terminal to form a frequency selective feedback network Causes Oscillations to Occur Amplifies the signal with the two negative feedback resistors 36

37 Basics About the Wien-Bridge 37

38 Open-loop Analysis Operational amplifier gain G V 1( s) V s ( s) 1 + R 2 R 1 Z 1 ( s) R + s 1 C V o ( s) V 1 ( s) Z 2 ( s) Z 1 ( s) + Z 2 ( s) Z 2 ( s) R R + 1 s C 1 s C V o ( s) G V s ( s) s R s 2 R 2 C s R C + 1 C 38

39 Open-loop Analysis Simplifying and substituting jw for s T( jω) j ω R C G ( 1 ω 2 R 2 C 2 ) + 3 j ω R C In order to have a phase shift of zero, 1 ω 2 R 2 C 2 0 This happens at ω = 1/ RC When ω = 1/RC, T(j ω) simplifies to: T( jω) G 3 If G = 3, sustained oscillations If G < 3, oscillations attenuate If G > 3, oscillations amplify 39

40 4.0V G = 3 0V -4.0V 0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0ms V(R5:2) Time 4.0V G = 2.9 0V -4.0V 0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0ms V(R5:2) Time 20V G = V -20V 0s 100us 200us 300us 400us 500us 600us V(R5:2) Time 40

41 Making the Oscillations Steady Add a diode network to keep circuit around G = 3 If G = 3, diodes are off 41

42 Results of Diode Network With the use of diodes, the non-ideal opamp can produce steady oscillations. 4.0V 0V -4.0V 0s 0.2ms 0.4ms 0.6ms 0.8ms 1.0ms V(D2:2) Time 42

43 Wireless applications Design Issues Tuning Range need to cover all frequency channels Noise impacts receiver blocking and sensitivity performance Power want low power dissipation Isolation want to minimize noise pathways into VCO Sensitivity to process/temp variations need to make it manufacturable in high volume High speed data link Required noise performance is often less stringent Tuning range is often narrower 43

44 Phase Noise and Timing Jitter Phase noise and timing jitter Phase noise Measure of spectral density of clock frequency Units: dbc/hz (decibels below the carrier per Hz) Analog people care about this Timing Jitter Measurement of clock transition edge to reference Units: Seconds (usually ps) More intuitive, useful in digital systems 44

45 Phase Noise and Timing Jitter Ring oscillators a general purpose building block in many areas of integrated circuit design Clock and Data Recovery On-Chip Clock Distribution Frequency Synthesis Data Conversion: Pulse Width and Phase Modulation 5-Stage Ring Oscillator Timing jitter and phase noise analysis is important Real Design Considerations: frequency, power, timing jitter The approach of supply and body bias voltage scaling 45

46 Timing Jitter and Phase Noise in Ring Oscillator Modified linear model of a five stage ring oscillator Two dominant types of noise in a ring oscillator transistor thermal noise power supply noise Noise effect modeling: current or charge injected into the load capacitance at each stage Noise q Cnode = V Φ Jitter! 46

47 Noise in Oscillators ( t φ) Vo,ideal = A cos ω o + V o,practical ( ) f ( ω t + φ( )) = A t o t periodic function with period= 2π f v n AM PM ω o ω o ω m FM ω o ω m ω o + ω m ω o AM ω o + ω m PM 47

48 Phase Noise Power ω 0 ω dbc 1Hz Freq Phase Noise f 4 (random walk FM) f 3 (flicker FM) f 2 (random walk phase or white FM) f -1 (flicker phase) f 0 (white phase) Frequency L total { ω} ( ω + ω Hz) Psideband 0 1, = 10 log Pcarrier 48

49 49 Phase Noise Phase noise is inversely proportional to power dissipation The higher the Q of the tank, the lower the phase noise { } + + = ω ω ω ω ω log 10 f P s Q L FkT L